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    Isotonicity of the Metric Projection and Complementarity Problems in Hilbert Spaces

    Access Status
    Fulltext not available
    Authors
    Kong, D.
    Liu, Lishan
    Wu, Yong Hong
    Date
    2017
    Type
    Journal Article
    
    Metadata
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    Citation
    Kong, D. and Liu, L. and Wu, Y.H. 2017. Isotonicity of the Metric Projection and Complementarity Problems in Hilbert Spaces. Journal of Optimization Theory and Applications: pp. 1-15.
    Source Title
    Journal of Optimization Theory and Applications
    DOI
    10.1007/s10957-017-1162-8
    ISSN
    0022-3239
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/57925
    Collection
    • Curtin Research Publications
    Abstract

    © 2017 Springer Science+Business Media, LLC In this paper, as the extension of the isotonicity of the metric projection, the isotonicity characterizations with respect to two arbitrary order relations induced by cones of the metric projection operator are studied in Hilbert spaces, when one cone is a subdual cone and some relations between the two orders hold. Moreover, if the metric projection is not isotone in the whole space, we prove that the metric projection is isotone in some domains in both Hilbert lattices and Hilbert quasi-lattices. By using the isotonicity characterizations with respect to two arbitrary order relations of the metric projection, some solvability and approximation theorems for the complementarity problems are obtained. Our results generalize and improve various recent results in the field of study.

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